Problem: A big football championship will occur soon! n teams will compete in it, and each pair of teams will play exactly one game against each other.

There are two possible outcomes of a game:

  * the game may result in a tie, then both teams get 1 point; 
  * one team might win in a game, then the winning team gets 3 points and the losing team gets 0 points. 



The score of a team is the number of points it gained during all games that it played.

You are interested in a hypothetical situation when all teams get the same score at the end of the championship. A simple example of that situation is when all games result in ties, but you want to minimize the number of ties as well.

Your task is to describe a situation (choose the result of each game) so that all teams get the same score, and the number of ties is the minimum possible.

Input

The first line contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

Then the test cases follow. Each test case is described by one line containing one integer n (2 ≤ n ≤ 100) — the number of teams.

Output

For each test case, print (n(n - 1))/(2) integers describing the results of the games in the following order: the first integer should correspond to the match between team 1 and team 2, the second — between team 1 and team 3, then 1 and 4, ..., 1 and n, 2 and 3, 2 and 4, ..., 2 and n, and so on, until the game between the team n - 1 and the team n.

The integer corresponding to the game between the team x and the team y should be 1 if x wins, -1 if y wins, or 0 if the game results in a tie.

All teams should get the same score, and the number of ties should be the minimum possible. If there are multiple optimal answers, print any of them. It can be shown that there always exists a way to make all teams have the same score.

Example

Input


2
2
3


Output


0 
1 -1 1 

Note

In the first test case of the example, both teams get 1 point since the game between them is a tie.

In the second test case of the example, team 1 defeats team 2 (team 1 gets 3 points), team 1 loses to team 3 (team 3 gets 3 points), and team 2 wins against team 3 (team 2 gets 3 points).

Solution (in PYTHON3):

Solution:
def divisors(M):
    d=[]
    i=1
    while M>=i**2:
        if M%i==0:
            d.append(i)
            if i**2!=M:
                d.append(M//i)
        i=i+1
    return d

def popcount(x):
    x = x - ((x >> 1) & 0x55555555)
    x = (x & 0x33333333) + ((x >> 2) & 0x33333333)
    x = (x + (x >> 4)) & 0x0f0f0f0f
    x = x + (x >> 8)
    x = x + (x >> 16)
    return x & 0x0000007f

def eratosthenes(n):
    res=[0 for i in range(n+1)]
    prime=set([])
    for i in range(2,n+1):
        if not res[i]:
            prime.add(i)
            for j in range(1,n//i+1):
                res[i*j]=1
    return prime

def factorization(n):
    res=[]
    for p in prime:
        if n%p==0:
            while n%p==0:
                n//=p
            res.append(p)
    if n!=1:
        res.append(n)
    return res

def euler_phi(n):
    res = n
    for x in range(2,n+1):
        if x ** 2 > n:
            break
        if n%x==0:
            res = res//x * (x-1)
            while n%x==0:
                n //= x
    if n!=1:
        res = res//n * (n-1)
    return res

def ind(b,n):
    res=0
    while n%b==0:
        res+=1
        n//=b
    return res

def isPrimeMR(n):
    d = n - 1
    d = d // (d & -d)
    L = [2, 3, 5, 7, 11, 13, 17]
    for a in L:
        t = d
        y = pow(a, t, n)
        if y == 1: continue
        while y != n - 1:
            y = (y * y) % n
            if y == 1 or t == n - 1: return 0
            t <<= 1
    return 1
def findFactorRho(n):
    from math import gcd
    m = 1 << n.bit_length() // 8
    for c in range(1, 99):
        f = lambda x: (x * x + c) % n
        y, r, q, g = 2, 1, 1, 1
        while g == 1:
            x = y
            for i in range(r):
                y = f(y)
            k = 0
            while k < r and g == 1:
                ys = y
                for i in range(min(m, r - k)):
                    y = f(y)
                    q = q * abs(x - y) % n
                g = gcd(q, n)
                k += m
            r <<= 1
        if g == n:
            g = 1
            while g == 1:
                ys = f(ys)
                g = gcd(abs(x - ys), n)
        if g < n:
            if isPrimeMR(g): return g
            elif isPrimeMR(n // g): return n // g
            return findFactorRho(g)
def primeFactor(n):
    i = 2
    ret = {}
    rhoFlg = 0
    while i*i <= n:
        k = 0
        while n % i == 0:
            n //= i
            k += 1
        if k: ret[i] = k
        i += 1 + i % 2
        if i == 101 and n >= 2 ** 20:
            while n > 1:
                if isPrimeMR(n):
                    ret[n], n = 1, 1
                else:
                    rhoFlg = 1
                    j = findFactorRho(n)
                    k = 0
                    while n % j == 0:
                        n //= j
                        k += 1
                    ret[j] = k

    if n > 1: ret[n] = 1
    if rhoFlg: ret = {x: ret[x] for x in sorted(ret)}
    return ret

def divisors(n):
    res = [1]
    prime = primeFactor(n)
    for p in prime:
        newres = []
        for d in res:
            for j in range(prime[p]+1):
                newres.append(d*p**j)
        res = newres
    res.sort()
    return res

def floor_sum(n: int, m: int, a: int, b: int) -> int:
    ans = 0

    if a >= m:
        ans += (n - 1) * n * (a // m) // 2
        a %= m

    if b >= m:
        ans += n * (b // m)
        b %= m

    y_max = (a * n + b) // m
    x_max = y_max * m - b

    if y_max == 0:
        return ans

    ans += (n - (x_max + a - 1) // a) * y_max
    ans += floor_sum(y_max, a, m, (a - x_max % a) % a)

    return ans

def xorfactorial(num):#排他的論理和の階乗
    if num==0:
        return 0
    elif num==1:
        return 1
    elif num==2:
        return 3
    elif num==3:
        return 0
    else:
        x=baseorder(num)
        return (2**x)*((num-2**x+1)%2)+function(num-2**x)

def xorconv(n,X,Y):
    if n==0:
        res=[(X[0]*Y[0])%mod]
        return res
    x=[X[i]+X[i+2**(n-1)] for i in range(2**(n-1))]
    y=[Y[i]+Y[i+2**(n-1)] for i in range(2**(n-1))]
    z=[X[i]-X[i+2**(n-1)] for i in range(2**(n-1))]
    w=[Y[i]-Y[i+2**(n-1)] for i in range(2**(n-1))]
    res1=xorconv(n-1,x,y)
    res2=xorconv(n-1,z,w)
    former=[(res1[i]+res2[i])*inv for i in range(2**(n-1))]
    latter=[(res1[i]-res2[i])*inv for i in range(2**(n-1))]
    former=list(map(lambda x:x%mod,former))
    latter=list(map(lambda x:x%mod,latter))
    return former+latter

def merge_sort(A,B):
    pos_A,pos_B = 0,0
    n,m = len(A),len(B)
    res = []
    while pos_A < n and pos_B < m:
        a,b = A[pos_A],B[pos_B]
        if a < b:
            res.append(a)
            pos_A += 1
        else:
            res.append(b)
            pos_B += 1
    res += A[pos_A:]
    res += B[pos_B:]
    return res

class UnionFindVerSize():
    def __init__(self, N):
        self._parent = [n for n in range(0, N)]
        self._size = [1] * N
        self.group = N

    def find_root(self, x):
        if self._parent[x] == x: return x
        self._parent[x] = self.find_root(self._parent[x])
        stack = [x]
        while self._parent[stack[-1]]!=stack[-1]:
            stack.append(self._parent[stack[-1]])
        for v in stack:
            self._parent[v] = stack[-1]
        return self._parent[x]

    def unite(self, x, y):
        gx = self.find_root(x)
        gy = self.find_root(y)
        if gx == gy: return

        self.group -= 1

        if self._size[gx] < self._size[gy]:
            self._parent[gx] = gy
            self._size[gy] += self._size[gx]
        else:
            self._parent[gy] = gx
            self._size[gx] += self._size[gy]

    def get_size(self, x):
        return self._size[self.find_root(x)]

    def is_same_group(self, x, y):
        return self.find_root(x) == self.find_root(y)

class WeightedUnionFind():
    def __init__(self,N):
        self.parent = [i for i in range(N)]
        self.size = [1 for i in range(N)]
        self.val = [0 for i in range(N)]
        self.flag = True
        self.edge = [[] for i in range(N)]

    def dfs(self,v,pv):
        stack = [(v,pv)]
        new_parent = self.parent[pv]
        while stack:
            v,pv = stack.pop()
            self.parent[v] = new_parent
            for nv,w in self.edge[v]:
                if nv!=pv:
                    self.val[nv] = self.val[v] + w
                    stack.append((nv,v))

    def unite(self,x,y,w):
        if not self.flag:
            return
        if self.parent[x]==self.parent[y]:
            self.flag = (self.val[x] - self.val[y] == w)
            return

        if self.size[self.parent[x]]>self.size[self.parent[y]]:
            self.edge[x].append((y,-w))
            self.edge[y].append((x,w))
            self.size[x] += self.size[y]
            self.val[y] = self.val[x] - w
            self.dfs(y,x)
        else:
            self.edge[x].append((y,-w))
            self.edge[y].append((x,w))
            self.size[y] += self.size[x]
            self.val[x] = self.val[y] + w
            self.dfs(x,y)

class Dijkstra():
    class Edge():
        def __init__(self, _to, _cost):
            self.to = _to
            self.cost = _cost

    def __init__(self, V):
        self.G = [[] for i in range(V)]
        self._E = 0
        self._V = V

    @property
    def E(self):
        return self._E

    @property
    def V(self):
        return self._V

    def add(self, _from, _to, _cost):
        self.G[_from].append(self.Edge(_to, _cost))
        self._E += 1

    def shortest_path(self, s):
        import heapq
        que = []
        d = [10**15] * self.V
        d[s] = 0
        heapq.heappush(que, (0, s))

        while len(que) != 0:
            cost, v = heapq.heappop(que)
            if d[v] < cost: continue

            for i in range(len(self.G[v])):
                e = self.G[v][i]
                if d[e.to] > d[v] + e.cost:
                    d[e.to] = d[v] + e.cost
                    heapq.heappush(que, (d[e.to], e.to))
        return d

#Z[i]:length of the longest list starting from S[i] which is also a prefix of S
#O(|S|)
def Z_algorithm(s):
    N = len(s)
    Z_alg = [0]*N

    Z_alg[0] = N
    i = 1
    j = 0
    while i < N:
        while i+j < N and s[j] == s[i+j]:
            j += 1
        Z_alg[i] = j
        if j == 0:
            i += 1
            continue
        k = 1
        while i+k < N and k + Z_alg[k]<j:
            Z_alg[i+k] = Z_alg[k]
            k += 1
        i += k
        j -= k
    return Z_alg

class BIT():
    def __init__(self,n):
        self.BIT=[0]*(n+1)
        self.num=n

    def query(self,idx):
        res_sum = 0
        while idx > 0:
            res_sum += self.BIT[idx]
            idx -= idx&(-idx)
        return res_sum

    #Ai += x O(logN)
    def update(self,idx,x):
        while idx <= self.num:
            self.BIT[idx] += x
            idx += idx&(-idx)
        return

class dancinglink():
    def __init__(self,n,debug=False):
        self.n = n
        self.debug = debug
        self._left = [i-1 for i in range(n)]
        self._right = [i+1 for i in range(n)]
        self.exist = [True for i in range(n)]

    def pop(self,k):
        if self.debug:
            assert self.exist[k]
        L = self._left[k]
        R = self._right[k]
        if L!=-1:
            if R!=self.n:
                self._right[L],self._left[R] = R,L
            else:
                self._right[L] = self.n
        elif R!=self.n:
            self._left[R] = -1
        self.exist[k] = False

    def left(self,idx,k=1):
        if self.debug:
            assert self.exist[idx]
        res = idx
        while k:
            res = self._left[res]
            if res==-1:
                break
            k -= 1
        return res

    def right(self,idx,k=1):
        if self.debug:
            assert self.exist[idx]
        res = idx
        while k:
            res = self._right[res]
            if res==self.n:
                break
            k -= 1
        return res

class SparseTable():
    def __init__(self,A,merge_func,ide_ele):
        N=len(A)
        n=N.bit_length()
        self.table=[[ide_ele for i in range(n)] for i in range(N)]
        self.merge_func=merge_func

        for i in range(N):
            self.table[i][0]=A[i]

        for j in range(1,n):
            for i in range(0,N-2**j+1):
                f=self.table[i][j-1]
                s=self.table[i+2**(j-1)][j-1]
                self.table[i][j]=self.merge_func(f,s)

    def query(self,s,t):
        b=t-s+1
        m=b.bit_length()-1
        return self.merge_func(self.table[s][m],self.table[t-2**m+1][m])

class BinaryTrie:
    class node:
        def __init__(self,val):
            self.left = None
            self.right = None
            self.max = val

    def __init__(self):
        self.root = self.node(-10**15)

    def append(self,key,val):
        pos = self.root
        for i in range(29,-1,-1):
            pos.max = max(pos.max,val)
            if key>>i & 1:
                if pos.right is None:
                    pos.right = self.node(val)
                    pos = pos.right
                else:
                    pos = pos.right
            else:
                if pos.left is None:
                    pos.left = self.node(val)
                    pos = pos.left
                else:
                    pos = pos.left
        pos.max = max(pos.max,val)

    def search(self,M,xor):
        res = -10**15
        pos = self.root
        for i in range(29,-1,-1):
            if pos is None:
                break

            if M>>i & 1:
                if xor>>i & 1:
                    if pos.right:
                        res = max(res,pos.right.max)
                    pos = pos.left
                else:
                    if pos.left:
                        res = max(res,pos.left.max)
                    pos = pos.right
            else:
                if xor>>i & 1:
                    pos = pos.right
                else:
                    pos = pos.left

        if pos:
            res = max(res,pos.max)
        return res

def solveequation(edge,ans,n,m):
    #edge=[[to,dire,id]...]
    x=[0]*m
    used=[False]*n
    for v in range(n):
        if used[v]:
            continue
        y = dfs(v)
        if y!=0:
            return False
    return x

    def dfs(v):
        used[v]=True
        r=ans[v]
        for to,dire,id in edge[v]:
            if used[to]:
                continue
            y=dfs(to)
            if dire==-1:
                x[id]=y
            else:
                x[id]=-y
            r+=y
        return r

class Matrix():
    mod=10**9+7

    def set_mod(m):
        Matrix.mod=m

    def __init__(self,L):
        self.row=len(L)
        self.column=len(L[0])
        self._matrix=L
        for i in range(self.row):
            for j in range(self.column):
                self._matrix[i][j]%=Matrix.mod

    def __getitem__(self,item):
        if type(item)==int:
            raise IndexError("you must specific row and column")
        elif len(item)!=2:
            raise IndexError("you must specific row and column")

        i,j=item
        return self._matrix[i][j]

    def __setitem__(self,item,val):
        if type(item)==int:
            raise IndexError("you must specific row and column")
        elif len(item)!=2:
            raise IndexError("you must specific row and column")

        i,j=item
        self._matrix[i][j]=val

    def __add__(self,other):
        if (self.row,self.column)!=(other.row,other.column):
            raise SizeError("sizes of matrixes are different")

        res=[[0 for j in range(self.column)] for i in range(self.row)]
        for i in range(self.row):
            for j in range(self.column):
                res[i][j]=self._matrix[i][j]+other._matrix[i][j]
                res[i][j]%=Matrix.mod
        return Matrix(res)

    def __sub__(self,other):
        if (self.row,self.column)!=(other.row,other.column):
            raise SizeError("sizes of matrixes are different")

        res=[[0 for j in range(self.column)] for i in range(self.row)]
        for i in range(self.row):
            for j in range(self.column):
                res[i][j]=self._matrix[i][j]-other._matrix[i][j]
                res[i][j]%=Matrix.mod
        return Matrix(res)

    def __mul__(self,other):
        if type(other)!=int:
            if self.column!=other.row:
                raise SizeError("sizes of matrixes are different")

            res=[[0 for j in range(other.column)] for i in range(self.row)]
            for i in range(self.row):
                for j in range(other.column):
                    temp=0
                    for k in range(self.column):
                        temp+=self._matrix[i][k]*other._matrix[k][j]
                    res[i][j]=temp%Matrix.mod
            return Matrix(res)
        else:
            n=other
            res=[[(n*self._matrix[i][j])%Matrix.mod for j in range(self.column)] for i in range(self.row)]
            return Matrix(res)

    def __pow__(self,m):
        if self.column!=self.row:
            raise MatrixPowError("the size of row must be the same as that of column")

        n=self.row
        res=Matrix([[int(i==j) for i in range(n)] for j in range(n)])
        while m:
            if m%2==1:
                res=res*self
            self=self*self
            m//=2
        return res

    def __str__(self):
        res=[]
        for i in range(self.row):
            for j in range(self.column):
                res.append(str(self._matrix[i][j]))
                res.append(" ")
            res.append("\n")
        res=res[:len(res)-1]
        return "".join(res)

class SegmentTree:
    def __init__(self, init_val, segfunc, ide_ele):
        n = len(init_val)
        self.segfunc = segfunc
        self.ide_ele = ide_ele
        self.num = 1 << (n - 1).bit_length()
        self.tree = [ide_ele] * 2 * self.num
        for i in range(n):
            self.tree[self.num + i] = init_val[i]
        for i in range(self.num - 1, 0, -1):
            self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])

    def update(self, k, x):
        k += self.num
        self.tree[k] = x
        while k > 1:
            self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
            k >>= 1

    def query(self, l, r):
        res = self.ide_ele

        l += self.num
        r += self.num
        while l < r:
            if l & 1:
                res = self.segfunc(res, self.tree[l])
                l += 1
            if r & 1:
                res = self.segfunc(res, self.tree[r - 1])
            l >>= 1
            r >>= 1
        return res

    def bisect_l(self,l,r,x):
        l += self.num
        r += self.num
        Lmin = -1
        Rmin = -1
        while l<r:
            if l & 1:
                if self.tree[l] <= x and Lmin==-1:
                    Lmin = l
                l += 1
            if r & 1:
                if self.tree[r-1] <=x:
                    Rmin = r-1
            l >>= 1
            r >>= 1

        if Lmin != -1:
            pos = Lmin
            while pos<self.num:
                if self.tree[2 * pos] <=x:
                    pos = 2 * pos
                else:
                    pos = 2 * pos +1
            return pos-self.num
        elif Rmin != -1:
            pos = Rmin
            while pos<self.num:
                if self.tree[2 * pos] <=x:
                    pos = 2 * pos
                else:
                    pos = 2 * pos +1
            return pos-self.num
        else:
            return -1

class DualSegmentTree:
    def __init__(self, n, segfunc, ide_ele):
        self.segfunc = segfunc
        self.ide_ele = ide_ele
        self.num = 1 << (n - 1).bit_length()
        self.tree = [ide_ele] * 2 * self.num

    def update(self,l,r,x):
        l += self.num
        r += self.num
        while l < r:
            if l & 1:
                self.tree[l] = self.segfunc(self.tree[l],x)
                l += 1
            if r & 1:
                self.tree[r-1] = self.segfunc(self.tree[r-1],x)
            l >>= 1
            r >>= 1

    def __getitem__(self,idx):
        idx += self.num
        res = self.ide_ele
        while idx:
            res = self.segfunc(res,self.tree[idx])
            idx>>=1
        return res

class LazySegmentTree():
    __slots__ = ["merge","merge_unit","operate","merge_operate","operate_unit","n","data","lazy"]
    def __init__(self,n,init,merge,merge_unit,operate,merge_operate,operate_unit):
        self.merge=merge
        self.merge_unit=merge_unit
        self.operate=operate
        self.merge_operate=merge_operate
        self.operate_unit=operate_unit

        self.n=(n-1).bit_length()
        self.data=[merge_unit for i in range(1<<(self.n+1))]
        self.lazy=[operate_unit for i in range(1<<(self.n+1))]
        if init:
            for i in range(n):
                self.data[2**self.n+i]=init[i]
            for i in range(2**self.n-1,0,-1):
                self.data[i]=self.merge(self.data[2*i],self.data[2*i+1])

    def propagate(self,v):
        ope = self.lazy[v]
        if ope == self.operate_unit:
            return
        self.lazy[v]=self.operate_unit
        self.data[(v<<1)]=self.operate(self.data[(v<<1)],ope)
        self.data[(v<<1)+1]=self.operate(self.data[(v<<1)+1],ope)
        self.lazy[v<<1]=self.merge_operate(self.lazy[(v<<1)],ope)
        self.lazy[(v<<1)+1]=self.merge_operate(self.lazy[(v<<1)+1],ope)

    def propagate_above(self,i):
        m=i.bit_length()-1
        for bit in range(m,0,-1):
            v=i>>bit
            self.propagate(v)

    def remerge_above(self,i):
        while i:
            c = self.merge(self.data[i],self.data[i^1])
            i>>=1
            self.data[i]=self.operate(c,self.lazy[i])

    def update(self,l,r,x):
        l+=1<<self.n
        r+=1<<self.n
        l0=l//(l&-l)
        r0=r//(r&-r)-1
        self.propagate_above(l0)
        self.propagate_above(r0)
        while l<r:
            if l&1:
                self.data[l]=self.operate(self.data[l],x)
                self.lazy[l]=self.merge_operate(self.lazy[l],x)
                l+=1
            if r&1:
                self.data[r-1]=self.operate(self.data[r-1],x)
                self.lazy[r-1]=self.merge_operate(self.lazy[r-1],x)
            l>>=1
            r>>=1
        self.remerge_above(l0)
        self.remerge_above(r0)

    def query(self,l,r):
        l+=1<<self.n
        r+=1<<self.n
        l0=l//(l&-l)
        r0=r//(r&-r)-1
        self.propagate_above(l0)
        self.propagate_above(r0)
        res=self.merge_unit
        while l<r:
            if l&1:
                res=self.merge(res,self.data[l])
                l+=1
            if r&1:
                res=self.merge(res,self.data[r-1])
            l>>=1
            r>>=1
        return res

    def bisect_l(self,l,r,x):
        l += 1<<self.n
        r += 1<<self.n
        l0=l//(l&-l)
        r0=r//(r&-r)-1
        self.propagate_above(l0)
        self.propagate_above(r0)
        Lmin = -1
        Rmin = -1
        while l<r:
            if l & 1:
                if self.data[l][0] <= x and Lmin==-1:
                    Lmin = l
                l += 1
            if r & 1:
                if self.data[r-1][0] <=x:
                    Rmin = r-1
            l >>= 1
            r >>= 1

        res = -1
        if Lmin != -1:
            pos = Lmin
            while pos<self.num:
                self.propagate(pos)
                if self.data[2 * pos][0] <=x:
                    pos = 2 * pos
                else:
                    pos = 2 * pos +1
            res =  pos-self.num
        if Rmin != -1:
            pos = Rmin
            while pos<self.num:
                self.propagate(pos)
                if self.data[2 * pos][0] <=x:
                    pos = 2 * pos
                else:
                    pos = 2 * pos +1
            if res==-1:
                res = pos-self.num
            else:
                res = min(res,pos-self.num)

        return res

import sys
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import permutations
from math import log,gcd

input = lambda :sys.stdin.readline().rstrip()
mi = lambda :map(int,input().split())
li = lambda :list(mi())

for _ in range(int(input())):
    n = int(input())
    ans = []
    if n%2==1:
        for i in range(1,n+1):
            for j in range(i+1,n+1):
                if (i+j)%2==1:
                    ans.append(1)
                else:
                    ans.append(-1)
    else:
        for i in range(1,n+1):
            for j in range(i+1,n+1):
                if i%2==1 and j==i+1:
                    ans.append(0)
                elif (i+j)%2==0:
                    ans.append(1)
                else:
                    ans.append(-1)
    print(*ans)